Binary Finite Field Extensions for Diffusion Matrices Over the Finite Field F2m

Abstract

In this paper, a new software tool has been developed that computes the corresponding m x m binary matrix over the finite field F-2 of each element which is defined over F-2m (where 3 <= m <= 8) generated by different primitive irreducible polynomials. This extension process is necessary for the optimization of XOR (exclusive OR) counts of diffusion matrices whose elements are defined over the finite field, which are used especially in the diffusion layers of block ciphers. Therefore, the corresponding binary matrices given in this study can be used directly for the construction of new diffusion matrices.